Oblique derivative problems in Lipschitz domains: II. Discontinuous boundary data.

for functions / and g in suitable weighted Holder classes. When β is continuous and oblique on 3 Ω and appropriate additional assumptions are made, various existence, uniqueness and regularity results were proved in [14]. Important technical difficulties arise for discontinuous β which were not present in [14]. For example, the boundary condition has to be suitably interpreted at points of discontinuity of . Because of these difficulties, we consider only the case that β and d Ω are piecewise smooth. Our basic result is the following theorem.